Clifford operators represent one of the most useful and one of the most studied subclass of quantum operators. Clifford operators are involved in numerous applications such as quantum error correction [1]}, randomized benchmarking protocols [2]}, [3]}, quantum state distillation [4]}, [5]}, the study of entanglement [6]}. It is known that Clifford operators can be generated by the Hadamard gates, the Phase gates and the CNOT gate [7]}. Moreover the simulation of such circuits, the so-called Clifford circuits, can be done efficiently on a classical computer [8]} and there is a one-to-one mapping between the Clifford operators and the \(2n \times 2n\)  binary matrices from the symplectic group \(Sp(2n, \mathbb {F}_2)\) .
